Deterministic Mean-field Ensemble Kalman Filtering
Abstract
The proof of convergence of the standard ensemble Kalman filter (EnKF) from Legland etal. (2011) is extended to non-Gaussian state space models. A density-based deterministic approximation of the mean-field limit EnKF (DMFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF when the dimension . The fidelity of approximation of the true distribution is also established using an extension of total variation metric to random measures. This is limited by a Gaussian bias term arising from non-linearity/non-Gaussianity of the model, which exists for both DMFEnKF and standard EnKF. Numerical results support and extend the theory.
Cite
@article{arxiv.1409.0628,
title = {Deterministic Mean-field Ensemble Kalman Filtering},
author = {Kody J. H. Law and Hamidou Tembine and Raul Tempone},
journal= {arXiv preprint arXiv:1409.0628},
year = {2016}
}